Brauer Groups and the Cohomology of Graded Rings PDF Download

Author: Stefaan Caenepeel
Publisher: CRC Press
ISBN: 1000103781
Category : Mathematics
Languages : en
Pages : 280

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Book Description
This book introduces various notions defined in graded terms extending the notions most frequently used as basic ingredients in the theory of Azumaya algebras: separability and Galois extensions of commutative rings, crossed products and Galois cohomology, Picard groups, and the Brauer group.

Author: Stefaan Caenepeel
Publisher: CRC Press
ISBN: 1000153282
Category : Mathematics
Languages : en
Pages : 352

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Book Description
"Based on papers presented at a recent international conference on algebra and algebraic geometry held jointly in Antwerp and Brussels, Belgium. Presents both survey and research articles featuring new results from the intersection of algebra and geometry. "

Author: Jean-Pierre Tignol
Publisher: Springer
ISBN: 3319163604
Category : Mathematics
Languages : en
Pages : 652

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Book Description
This monograph is the first book-length treatment of valuation theory on finite-dimensional division algebras, a subject of active and substantial research over the last forty years. Its development was spurred in the last decades of the twentieth century by important advances such as Amitsur's construction of non crossed products and Platonov's solution of the Tannaka-Artin problem. This study is particularly timely because it approaches the subject from the perspective of associated graded structures. This new approach has been developed by the authors in the last few years and has significantly clarified the theory. Various constructions of division algebras are obtained as applications of the theory, such as noncrossed products and indecomposable algebras. In addition, the use of valuation theory in reduced Whitehead group calculations (after Hazrat and Wadsworth) and in essential dimension computations (after Baek and Merkurjev) is showcased. The intended audience consists of graduate students and research mathematicians.

Author: Stefaan Caenepeel
Publisher: Springer Science & Business Media
ISBN: 9781402003462
Category : Mathematics
Languages : en
Pages : 516

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Book Description
This volume is devoted to the Brauer group of a commutative ring and related invariants. Part I presents a new self-contained exposition of the Brauer group of a commutative ring. Included is a systematic development of the theory of Grothendieck topologies and étale cohomology, and discussion of topics such as Gabber's theorem and the theory of Taylor's big Brauer group of algebras without a unit. Part II presents a systematic development of the Galois theory of Hopf algebras with special emphasis on the group of Galois objects of a cocommutative Hopf algebra. The development of the theory is carried out in such a way that the connection to the theory of the Brauer group in Part I is made clear. Recent developments are considered and examples are included. The Brauer-Long group of a Hopf algebra over a commutative ring is discussed in Part III. This provides a link between the first two parts of the volume and is the first time this topic has been discussed in a monograph. Audience: Researchers whose work involves group theory. The first two parts, in particular, can be recommended for supplementary, graduate course use.

Author: S. Caenepeel
Publisher:
ISBN:
Category :
Languages : en
Pages : 166

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Book Description

Author: Constantin Nastasescu
Publisher: Springer Science & Business Media
ISBN: 9783540207467
Category : Mathematics
Languages : en
Pages : 324

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Book Description
The Category of Graded Rings.- The Category of Graded Modules.- Modules over Stronly Graded Rings.- Graded Clifford Theory.- Internal Homogenization.- External Homogenization.- Smash Products.- Localization of Graded Rings.- Application to Gradability.- Appendix A:Some Category Theory.- Appendix B: Dimensions in an abelian Category.- Bibliography.- Index.-

Author: Stefaan Caenepeel
Publisher: CRC Press
ISBN: 0429529988
Category : Mathematics
Languages : en
Pages : 332

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Book Description
This volume is based on the proceedings of the Hopf-Algebras and Quantum Groups conference at the Free University of Brussels, Belgium. It presents state-of-the-art papers - selected from over 65 participants representing nearly 20 countries and more than 45 lectures - on the theory of Hopf algebras, including multiplier Hopf algebras and quantum g

Author: Alexander J. Hahn
Publisher: Springer Science & Business Media
ISBN: 146846311X
Category : Mathematics
Languages : en
Pages : 296

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Book Description
Quadratic Algebras, Clifford Algebras, and Arithmetic Forms introduces mathematicians to the large and dynamic area of algebras and forms over commutative rings. The book begins very elementary and progresses gradually in its degree of difficulty. Topics include the connection between quadratic algebras, Clifford algebras and quadratic forms, Brauer groups, the matrix theory of Clifford algebras over fields, Witt groups of quadratic and symmetric bilinear forms. Some of the new results included by the author concern the representation of Clifford algebras, the structure of Arf algebra in the free case, connections between the group of isomorphic classes of finitely generated projectives of rank one and arithmetic results about the quadratic Witt group.

Author: Stefaan Caenepeel
Publisher: CRC Press
ISBN: 0429530072
Category : Mathematics
Languages : en
Pages : 348

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Book Description
This comprehensive reference summarizes the proceedings and keynote presentations from a recent conference held in Brussels, Belgium. Offering 1155 display equations, this volume contains original research and survey papers as well as contributions from world-renowned algebraists. It focuses on new results in classical Hopf algebras as well as the

Author: Jose L. Bueso
Publisher: Springer
ISBN: 3540392785
Category : Mathematics
Languages : en
Pages : 343

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Book Description
The papers in this proceedings volume are selected research papers in different areas of ring theory, including graded rings, differential operator rings, K-theory of noetherian rings, torsion theory, regular rings, cohomology of algebras, local cohomology of noncommutative rings. The book will be important for mathematicians active in research in ring theory.